Towards an accurate voxel-based analytic unified scatter and attenuation system model for 3D PET

A voxel-based approach to 3D PET analytic system modeling which projects the unit sphere of Klein-Nishina probabilities onto the cylindrical detection sphere, is proposed and under development. The aim is to offer the accuracy of a Monte Carlo model but without the noise and computational limitations. The model, incorporating both photon attenuation and scattering, defines PET system matrix elements based only on knowledge of a transmission scan and the specifications of a given PET system. No knowledge of the true activity is required to define the model. Reconstruction with such a unified analytic model makes full use of all the information contained in the measured data (both true and scatter events). No scatter subtraction, or scatter addition to the forward model output, are required. For 3D PET with large attenuating media, full use of the acquired information results in lower noise levels in the final image. The core of the technique models object scatter and attenuation via the Klein-Nishina cross-section and the transmission scan. However, the model must also include component-based normalization which accounts for scanner geometry as well as the crystal type and their arrangement.